Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  set<int> s;
  set<int>::iterator it;
  int i = 1;
  while (true) {
    long long t = (long long)i * (i + 1);
    t /= 2;
    if (t > 1e9) break;
    s.insert(t);
    i++;
  }
  int n;
  while (cin >> n) {
    bool y = false;
    for (it = s.begin(); it != s.end(); it++) {
      if (*it > n) break;
      if (s.find(n - *it) != s.end()) {
        y = true;
        break;
      }
    }
    if (y)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}